Computational Bayesian Approach to Proportional Hazards Model

4 COMPUTATIONAL BAYESIAN APPROACH TO PROPORTIONAL HAZARDS MODEL 

In the computational Bayesian approach, we want to draw a sample from the actual posterior, not its approximation. The proportional likelihood is given in Equation 9.7, and multiplying by the prior will give the true proportional posterior. Our approach 

We approximate the likelihood function by a multivariate normat[0ML ML] where 0ml MLE and Vml (he matched curvature covariance matrix that is output by the Iteratively reweighted least squares. We use a multivariate normal, Vo] prior for /3, or we can use a flat prior if we have no prior information. The approximate posterior will be 

Since both the prior and (approximate) likelihood are multivariate normal so will the approximate posterior. The updated constants will be 

Find the lower triangular matrix L such that satisfies 

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